### Browsing by Author "Yu, Wensheng"

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Item Edge theorem for multivariable systems(2002-10) Wang, Long; Wang, Zhizhen; Yu, WenshengShow more This paper studies robustness of multivariable systems with parametric uncertainties, and establishes a multivariable version of Edge Theorem. An illustrative example is presented.Show more Item General solution to the robust strictly positive real synthesis problem for polynomial segments(2002-10) Yu, Wensheng; Wang, LongShow more This paper constructively solves a long standing open problem in modern control theory. Namely, for any two n-th order polynomials a(s) and b(s), the Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial c(s) such that c(s) / a(s) and c(s) / b(s) are both strictly positive real.Show more Item Geometric characterization of strictly positive real regions and its applications(2002-02) Wang, Long; Yu, WenshengShow more Strict positive realness (SPR) is an important concept in absolute stability theory, adaptive control, system identification, etc. This paper characterizes the strictly positive real (SPR) regions in coefficient space and presents a robust design method for SPR transfer functions. We first introduce the concepts of SPR regions and weak SPR regions and show that the SPR region associated with a fixed polynomial is unbounded, whereas the weak SPR region is bounded. We then prove that the intersection of several weak SPR regions associated with different polynomials can not be a single point. Furthermore, we show how to construct a point in the SPR region from a point in the weak SPR region. Based on these theoretical development, we propose an algorithm for robust design of SPR transfer functions. This algorithm works well for both low order and high order polynomial families. Illustrative examples are provided to show the effectiveness of this algorithm.Show more Item Improved results on robust stability of multivariable interval control systems(2002-10) Wang, Zhizhen; Wang, Long; Yu, WenshengShow more For interval polynomial matrices, we identify the minimal testing set, whose stability can guarantee that of the whole uncertain set. Our results improve the conclusions given by Kamal and Dahleh.Show more Item On the number of positive solutions to a class of integral equations(2002-02) Wang, Long; Yu, Wensheng; Zhang, LinShow more Item Robust D-stability of uncertain MIMO systems: LMI criteria(2002-10) Yu, Wensheng; Wang, LongShow more The focal point of this paper is to provide some simple and efficient criteria to judge the D-stability of two families of polynomials, i.e., an interval multilinear polynomial matrix family and a polytopic polynomial family. Taking advantage of the uncertain parameter information, we analyze these two classes of uncertain models and give some LMI conditions for the robust stability of the two families. Two examples illustrate the effectiveness of our results.Show more Item Robust SPR synthesis for low-order polynomial segments and interval polynomials(2002-02) Wang, Long; Yu, WenshengShow more We prove that, for low-order (n 4) stable polynomial segments or interval polynomials, there always exists a fixed polynomial such that their ratio is SPR-invariant, thereby providing a rigorous proof of Anderson's claim on SPR synthesis for the fourth-order stable interval polynomials. Moreover, the relationship between SPR synthesis for low-order polynomial segments and SPR synthesis for low-order interval polynomials is also discussed.Show more Item Robust strictly positive real synthesis for convex combination of sixth-order polynomials, Wensheng Yu and Long Wang(2002-10) Yu, Wensheng; Wang, LongShow more For the two sixth-order polynomials a(s) and b(s), Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial c(s) such that c(s) / a(s) and c(s) / b(s) are both strictly positive real. Our reasoning method is constructive, and is insightful and helpful in solving the general robust strictly positive real synthesis problem.Show more Item Robust strictly positive real synthesis for polynomial families of arbitrary order(2002-10) Yu, Wensheng; Wang, LongShow more For any two n-th order polynomials a(s) and b(s), the Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial c(s) such that c(s) / a(s) and c(s) / b(s) are both strictly positive real.Show more Item Stability of polytopic polynomial matrices(2002-02) Wang, Long; Wang, Zhizhen; Yu, WenshengShow more This paper gives a necessary and sufficient condition for robust D-stability of Polytopic Polynomial Matrices.Show more